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In an examination of a certain class, at least 70% of the students failed in Physics, at least 72% failed in Chemistry, at least 80% failed in Mathematics and at least 85% failed in English. How many at least must have failed in all the four subjects ?

In an examination of a certain class, at least 70% of the students failed in Physics, at least 72% failed in Chemistry, at least 80% failed in Mathematics and at least 85% failed in English. How many at least must have failed in all the four subjects ? Correct Answer 7%

70 + 72 – t1 = 100

t1 = 42% ⇒ min. in P ∩ C = 42%

t2 = 85% – 20% = 65% ⇒ min. M ∩ E = 65%

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t = 42 – 35 = 7%

min. in ((P ∩ C) ∩ (M ∩ E)) = 7%

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